1. Unit 09 “The Law of the Conservation of Momentum” Group Problem Solving

2. (Easy) A 30kg lion jumps into a 75kg log at rest on the water. If the initial velocity of the lion is 5.00m/s as it jumps, what is the final velocity of the lion and the log? (Easy) A 60.0kg ice skater throws a 5.0kg snowball to the right with a speed of 15.0m/s, pushing the ice skater backwards. Assuming that the ice skater and snowball start from rest, find the final speed of the ice skater. (Medium) A 10.0kg blue cart moving to the right with a speed of 5.0m/s collides with a 5.0kg red cart moving to the left with a speed of 3.0m/s. After the blue cart moves to the left with a velocity of 2.0m/s, what is the velocity of the red cart? (Hard) A 95.0kg astronaut throws a 5.0kg ball to the right with a speed of 12.0m/s, how long does it take him to reach the shuttle 4.0m away? (Hard) A 2kg bullet is fired into a 5kg pendulum bob initially at rest. If the pendulum and bullet raise a vertical distance of 0.80m, what was the initial velocity of the bullet? Answer: 11m/s to the right Answer: -1.25 m/s (1.25m/s to the left) Answer: 1.43m/s Answer: 6.33 seconds Answer: 13.9m/s

3. (Easy) A 30kg lion jumps into a 75kg log at rest on the water. If the initial velocity of the lion is 5.00m/s as it jumps, what is the final velocity of the lion and the log? 1 2 1 2 m 1 = 30.0kg V 1 = 5.00m/s m 2 = 75kg V 2 = 0m/s m 1 V 1 + m 2 V 2 = (m 1 + m 2 )V f 150kgm/s = (105kg)V f 1.43m/s = V f 1 st Draw a Picture BeforeAfter (m 1 + m 2 )= 105kg V f = ? (30.0kg)(5.00m/s)+(75kg)(0m/s) = (105kg)(V f )

4. (Easy) A 60.0kg ice skater throws a 5.0kg snowball to the right with a speed of 15.0m/s, pushing the ice skater backwards. Assuming that the ice skater and snowball start from rest, find the final speed of the ice skater. BeforeAfter 1 st Draw a Picture 1 2 1 2 (m 1 + m 2 )= 65.0kg V i = 0m/s m 1 = 60.0kg V 1 = ? m 2 = 5.0kg V 2 = 15m/s (m 1 + m 2 )V i = m 1 V 1 + m 2 V 2 (65.0kg)(0m/s) = (60.0kg)V 1 + (5.0kg)(15.0m/s) 0kgm/s = (60.0kg)V 1 + 75.0kgm/s -75.0kgm/s = (60.0kg)V 1 -1.25m/s = V 1 +75kgm/s -75kgm/s

5. (Medium) A 10.0kg blue cart moving to the right with a speed of 5.0m/s collides with a 5.0kg red cart moving to the left with a speed of 3.0m/s. After the blue cart moves to the left with a velocity of 2.0m/s, what is the velocity of the red cart? BeforeAfter 1 2 1 2 m 1 = 10.0kg V 1 = 5.0m/s m 2 = 5.0kg V 2 = -3.0m/s m 1 V 1 + m 2 V 2 = m 1 V 1 + m 2 V 2 50kgm/s + (-15.0kgm/s) = -20kgm/s + (5kg)V 2 55kgm/s = (5kg)V 2 11m/s = V 2 35kgm/s = -20kgm/s + (5kg)V 2 m 1 = 10.0kg V 1 = -2.0m/s m 2 = 5.0kg V 2 = ? (10kg)(5m/s) + (5kg)(-3m/s) = (10kg)(-2m/s) + (5kg)(V 2 )

6. (Hard) A 95.0kg astronaut throws a 5.0kg ball to the right with a speed of 12.0m/s, how long does it take him to reach the shuttle 4.0m away? BeforeAfter 1 2 1 2 (m 1 + m 2 )= 100.0kg V i = 0m/s m 1 = 95.0kg V 1 = ? m 2 = 5.0kg V 2 = 12m/s (m 1 + m 2 )V i = m 1 V 1 + m 2 V 2 (100.0kg)(0m/s) = (95.0kg)V 1 + (5.0kg)(12.0m/s) 0kgm/s = (95.0kg)V 1 + 60.0kgm/s -60.0kgm/s = (95.0kg)V 1 -0.632m/s = V 1 +60kgm/s -60kgm/s Δx = -4.0m Δ t = ? V = _____ You need the velocity first! Find it by looking at the collision! -0.632m/s V = Δ x/ Δ t -0.632m/s = (- 4m) / Δ t Δ t = 6.33s (-) because he moves backwards.

7. (Hard) A 2kg bullet is fired into a 5kg pendulum bob initially at rest. If the pendulum and bullet raise a vertical distance of 0.80m, what was the initial velocity of the bullet? 1 2 1 m 1 = 2.0kg V 1 = ? m 2 = 5kg V 2 = 0m/s m 1 V 1 + m 2 V 2 = (m 1 + m 2 )V f 2kg(V 1 ) = 27.7kgm/s V 1 = 13.9m/s Before After (m 1 + m 2 )= 7kg V f = ? (2.0kg)(V 1 )+(5kg)(0m/s) = (7kg)(3.96m/s) Can’t solve for V 1 – initial velocity of bullet – if you don’t know the V f after the collision! 2 1 st : Find V after collision Δ y= 0.80m a = -9.8m/s 2 V f = 0m/s V i = ? V f 2 = V i 2 +2a Δ y (0m/s) 2 = V i 2 +2(-9.8m/s 2 ) (0.80m) (0m/s) 2 = V i 2 - 15.7m 2 /s 2 15.7m 2 /s 2 = V i 2 3.96m/s = V i 3.96m/s